# Quantum Mechanics [GATE (Graduate Aptitude Test in Engineering) Physics]: Questions 1 - 5 of 80

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## Question 1

Appeared in Year: *2014*

### Write in Short

Short Answer▾A hydrogen atom is in the state

Where in denote the principal, orbital and magnetic quantum numbers, respectively. If is the angular momentum operator, the average value of is________ .

## Question 2

Appeared in Year: *2014*

### Question

MCQ▾A particle is confined to a one dimensional potential box with the potential

If the particle is subjected to a perturbation, within the box, , where is a small constant, the first order correction to the ground state energy is –

### Choices

Choice (4) | Response | |
---|---|---|

a. | ||

b. | ||

c. | 0 | |

d. |

## Question 3

Appeared in Year: *2015*

### Question

MCQ▾The average energy of a one dimensional quantum oscillator of frequency and in contact with a heat bath at temperature T is given by,

### Choices

Choice (4) | Response | |
---|---|---|

a. | ||

b. | ||

c. | ||

d. |

## Question 4

Appeared in Year: *2015*

### Question

MCQ▾A particle is confined in a box of length as shown below,

If the potential is treated as a perturbation, including the first order correction, the ground state energy is –

### Choices

Choice (4) | Response | |
---|---|---|

a. | ||

b. | ||

c. | ||

d. |

## Question 5

Appeared in Year: *2014*

### Write in Short

Short Answer▾If and are the angular momentum ladder operators, then, the expectation value of , in the state of an atom is .